A rectangular box is to have a square base and a volume of 20 ft3. If the material for the base costs $0.35/ft2, the material for the sides costs $0.10/ft2, and the material for the top costs $0.15/ft2, determine the dimensions of the box that can be constructed at minimum cost.
length ft
width ft
height ft

Answer:

(3 , 1)

Step-by-step explanation:

3x - y = 8          -----------------(I)

x + 2y = 5   ------------(II)

Multiply (I) by 2 and then add. Thus y will be eliminates and we can find the value of x

(I)*2    6x - 2y = 16

(II)        x  + 2y = 5

          7x         = 21

            x       = 21/7

x = 3

Plugin x = 3 in equation (II)

3 + 2y = 5

      2y  = 5 - 3

      2y = 2

        y = 2/2

y = 1

Answer:

(3,1)

\(3x - y = 8(1) \\ x + 2y = 5(2) \\ from \: equation \:( 2 )\: \\ x = 5 - 2y \\ substitution \: in \: equation \: (1) \\ 3(5 - 2y) - y = 8 \\ 15 - 6y - y = 8 \\ - 7y = 8 - 15 \\ - 7y = - 7 \frac{ - 7y}{ - 7} = \frac{ - 7}{ - 7} \\ y = 1 \\ x = 5 - 2y \\ = 5 - 2(1) \\ = 5 - 2 \\ = 3 \\ (3 \: 1)\)

Step-by-step explanation:

HOPE THAT THIS HELPFUL .

HAVE A GREAT DAY.

Numbers written in scientific notation can be added, subtracted, multiplied and divided just like numbers in standard form.

Scientific notation is a way to write very large or very small numbers using exponents. The format of scientific notation is \(a * 10^n\) where a = number between 1 - 10 and n = integer.

When adding, subtracting, multiplying or dividing numbers in scientific notation, the exponents are manipulated by rules of arithmetic. For example, when adding or subtracting numbers in scientific notation, the exponents are made equal before adding or subtracting the coefficients.

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8400000cm

84 kilometer is 8400000 centimeter.

Here given 84 km ,

We know that 1 km = 1000 meter

               so 84 km  = 84 x 1000 meter

                                 = 84000 meter

 and 1 meter = 100 cm

 so here 84000 meter = 84000 x 100 cm

                                       = 8,400,000 Centimeters

∴ 84 km = 8400000cm

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Answer:

20.5

Step-by-step explanation:

AB= Sqare root of 15^2 + 14^2

USe pythagoras' theorum

An equation highlighting the discount: y = (65 - 7)x

A simpler equation: y = 58x

Answer:

x=-4.73 and -1.26

Step-by-step explanation:

We need to solve the given equation for x.

\((x + 3)^2 - 3 =0\)

Solving the above equation using formula (a+b)² =a²+2ab+b²

\((x + 3)^2 - 3 =0\\\\x^2+9+6x-3=0\\\\x^2+6x+6=0\)

It is a quadratic equation.

\(x=\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}\)

We have, a = 1, b = 6 and c = 6

\(x=\dfrac{-6\pm \sqrt{(6)^2-4\times 1\times 6} }{2\times 1}\\\\x=\dfrac{-6+\sqrt{(6)^{2}-4\times1\times6}}{2\times1},\dfrac{-6-\sqrt{(6)^{2}-4\times1\times6}}{2\times1}\\\\x=-1.267, -4.73\)

So, the values of x are -4.73 and -1.26

x^2 + 2xy + y^2 + 3x + 3y + 2

There are no like terms.

The union and intersection of n sets that are all subsets of the universal set u can be found using bit strings.

Bit strings are a way of representing sets as strings of binary digits. To represent a set, each element is assigned a digit of 0 or 1. A 1 indicates that the element is in the set, while a 0 indicates that the element is not in the set.

The union of the sets is found by combining the bit strings and setting any digit that is 1 in any of the sets to a 1. The intersection is found by comparing the bit strings and setting any digit that is 1 in all of the sets to a 1.

By using bit strings, we can quickly and accurately find the union and intersection of n sets that are all subsets of the universal set u.

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Answer: 106 yards

Step-by-step explanation: Find the square root of 702.25 which is 26.5, then times 26.5 by 4 to find the perimeter. 106 yards.

Answer:

106

Step-by-step explanation:

First, find the square root of 702.25 (26.5), then multiply that number by 4.

eat a peppermint it will stimulate your small brain

The probability of outcome to be a 5 is 1/13. The probability of outcome not be 5 is 12/13. The probability of outcome to be a diamond or a king is 4/13. The probability of the outcomes to be a jack or a queen is 2/13. The probability of The outcome to be a heart and a club is 0 and the probability of the outcomes to be a card greater than 6 and less than 9 is  2/13.

A deck contains a total of 52 cards.

Total outcomes if the selected number of cards is one=52

Case A:

Each suit contain one 5 numbered card. There are four suits. Therefore, The required outcome would be 4.

Probability of an outcome is the ratio of desired outcomes to the total outcomes.

The probability of outcome to be 5, P(A):
P(A)=4/52

P(A)=1/13

Case B:

The total probability of outcomes=52/52=1

The probability of the outcome to be 5=1/13

Therefore, the probability of the outcome not to be 5, P(B):

P(B)=1-(1/13)

P(B)=12/13

Case C:

Each suit carries a king. Therefore, the probability of the outcome to be a king, P(M):

P(M)=4/52

P(M)=1/13

A suit carries 13 cards. Therefore, there will be 13 cards of diamonds.

The probability of the outcome to be a diamond, P(N):

P(N)=13/52

P(N)=1/4

The probability that the outcome is a king of diamonds, P(M\(\cap\)N):

P(M\(\cap\)N)=1/52

Hence, the probability that the outcome is a diamond or a king, P(M\(\cup\)N):

P(M\(\cup\)N)=P(M)+P(N)-P(M\(\cap\)N)

P(M\(\cup\)N)=(1/13)+(1/4)-(1/52)

P(M\(\cup\)N)=16/52

P(M\(\cup\)N)=4/13

Case D:

Each suit carries a Jack. Therefore, the probability of the outcome to be a jack, P(P):

P(P)=4/52

P(P)=1/13

Each suit carries a Queen. Therefore, the probability of the outcome to be a Queen, P(Q):

P(Q)=4/52

P(Q)=1/13

The probability that the outcome is a jack and a queen, P(P\(\cap\)Q):

P(P\(\cap\)Q)=0/52

P(P\(\cap\)Q)=0

Hence, the probability that the outcome is a jack or a queen, P(P\(\cup\)Q):

P(P\(\cup\)Q)=P(P)+P(Q)-P(P\(\cap\)Q)

P(P\(\cup\)Q)=(1/13)+(1/13)-0

P(P\(\cup\)Q)=2/13

Case E:

A card is never a heart and a club. Therefore, the probability of a card to be a heart and a club is 0.

Case F:

The numbers greater than 6 and less than 9 are the numbers between 6 and 9. The numbers between 6 and 9 are 7 and 8.

Each suit carries one 7 numbered card and one 8 numbered card. There is a total of 4 suits.

Therefore the desirable outcomes=8

The probability of the outcome required=8/52

=2/13

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The function that represents the equation in table A is: f(x) = 6x + 15

The function that represents the equation in table B is: g(x) = -2x + 7

The formula to find the linear equation between two coordinates is expressed by the formula:

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

For table A, we are going to use two coordinates namely:

(0, 15) and (1, 21) and we have:

(y - 15)/(x - 0) = (21 - 15)/(1 - 0)

(y - 15)/x = 6

y - 15 = 6x

y = 6x + 15

For table B, we are going to use two coordinates namely:

(0, 7) and (1, 5)

Thus:

(y - 7)/(x - 0) = (5 - 7)/(1 - 0)

y - 7 = -2x

y = -2x + 7

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Answer: 5+5+12+12

Step-by-step explanation:

The normal distribution is approximately 65.328 minutes.

To find the value that separates the top 15% of the data from the bottom 85% in a normal distribution with a mean of 56 minutes and a standard deviation of 9 minutes, we can use the Z-score.

The Z-score represents the number of standard deviations a data point is from the mean. In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

To find the Z-score corresponding to the top 15% of the data, we need to find the Z-score that corresponds to the area of 0.15 in the tail of the distribution (above the mean).

Using a Z-table or a statistical calculator, we can find that the Z-score corresponding to the top 15% (above the mean) is approximately 1.0364.

To find the value that corresponds to this Z-score, we can use the formula:

Value = Mean + (Z-score * Standard Deviation)

Plugging in the values:

Mean = 56 minutes

Standard Deviation = 9 minutes

Z-score = 1.0364

Value = 56 + (1.0364 * 9)

Value = 56 + 9.328

Value ≈ 65.328

Therefore, the value (score) that separates the top 15% of the data from the bottom 85% for the given normal distribution is approximately 65.328 minutes.

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Answer:

The answer is 15 - p = k

Answer:

Janelle rides her bike at a rate of 0.25 km per minute.

Step-by-step explanation:

15 divided by 60 = 0.25

(I'm assuming this is an open question, if there are choices then put them in the comments and I'll edit the answer)

64 unique extensions are there with no repeated digits.

Combinations are decisions that are made by choosing some or all of a group of objects, regardless of how they are arranged.

For the 3-digit area code, the first digit can be any digit from 2 through 9, and each of the two digits that follow can be any digit from 0 through 9. That's a total of 8 × 10 × 10 = 800 different combinations.

Given:

A school district telephone system has three-digit extensions.

So,  first digit cannot be zero then we have possibility of total 8 digits.

and the last number is a nine.

unique extensions are there with no repeated digits

= 8 x 8 x 1

= 64

Hence, 64 unique extensions are there with no repeated digits.

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when x = -3

f(-3) = 5 5 is the result

Answer:

2 x 2+ 8 x 0= 4

Step-by-step explanation:

Answer:

c.16

hope this helps some one, have a nice day :)

Step-by-step explanation:

i just took the quiz and got it correct

Answer:

405

Step-by-step explanation:

5x9x9= 405

Answer:add 3

Step-by-step explanation:

Answer:

V= 314

Step-by-step explanation:

r = 5 in. ; h= 12 in.

Plug the numbers into the equation

\(\frac{1}{3}\left(3.14\right)\left(5^2\right)\left(12\right)\)

(^Ends here if you use calculator)

Multiply fractions \(\:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}\)

\(=3.14\cdot \frac{5^2\cdot \:1\cdot \:12}{3}\)

\(\frac{1*5^{2} *12}{3}=100\)

\(=100\cdot \:3.14\)

\(=314\)

9514 1404 393

Answer:

  4arcsin(x^(1/4)) +C

Step-by-step explanation:

Let x = z^4. Then dx = 4z^3·dz, and the given expression is ...

  \(\displaystyle\frac{dx}{\sqrt{x\sqrt{x}-x^2}}=\frac{4z^3\,dz}{\sqrt{z^4z^2-z^8}}=4\cdot\frac{dz}{\sqrt{1-z^2}}\)

and its integral is ...

  \(\displaystyle\int{\frac{4\,dz}{\sqrt{1-z^2}}}=4\arcsin{(z)}+C=\boxed{4\arcsin{\sqrt[4]{x}}+C}\)

__

Note that the original integrand is only defined on the interval (0, 1).

After considering the given data we conclude that there truth table is possible and is placed in the given figures concerning every sub question.

A truth table is a overview that projects  the truth-value of one or more compound propositions for each possible combination of truth-values of the propositions starting up the compound ones.
Every row of the table represents a possible combination of truth-values for the component propositions of the compound, and the count of rows is described by the range of possible combinations.
For instance, if the compound has just two component propositions, it comprises  four possibilities and then four rows to the table. The truth-value of the compound is projected on each row comprising the truth functional operator.
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Answer:

All you do is

Step-by-step explanation:

1/4 x 6

Then simplefiy your answer

Hey there!

6 * 1/4

= 6/1 * 1/4
= 6(1) / 1(4)

= 6 / 4

= 6 ÷ 2 / 4 ÷ 2

= 3 / 2

≈ 1 1/2

Therefore, your answer is: 1 1/2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

(a) The rate of change of P with respect to time is dP/dt = k(P^(1/3))^4.

(b) The solution of differential equation is P = (1/(1/3000 - t/9000000))^3.

(c) Whether or not this population size is cause for concern depends on various factors, such as the size of the swarm relative to the available resources in the surrounding environment etc.

(a) Let P(t) be the population of the swarm at time t. The rate of change of P with respect to time is proportional to the fourth power of the cubic root of its current population. Therefore, we have:

dP/dt = k(P^(1/3))^4

where k is a positive constant of proportionality.

(b) To solve the differential equation, we can use separation of variables:

dP/(P^(1/3))^4 = k dt

Integrating both sides, we get:

-3(P^(1/3))^(-3) / 3 = kt + C

where C is the constant of integration.

Using the initial condition that P(0) = 1000, we have:

-3(1000^(1/3))^(-3) / 3 = C

C = -1/3000

Substituting this value of C back into the equation, we get:

(P^(1/3))^(-3) = 1/3000 - kt/3

Raising both sides to the power of 3, we get:

P = (1/(1/3000 - kt/3))^3

Using the additional information that P(3) = 8000, we can solve for k:

8000 = (1/(1/3000 - 3k))^3

1/8000 = (1/3000 - 3k)

k = (1/9000000)

Substituting this value of k back into the equation, we get:

P = (1/(1/3000 - t/9000000))^3

(c) To determine if the concerns of the people of the nearby town are justified, we need to calculate the population of the swarm at t = 6 and compare it to some threshold value. Using the formula we derived in part (b), we have:

P(6) = (1/(1/3000 - 6/9000000))^3

P(6) ≈ 513,800

Whether or not this population size is cause for concern depends on various factors, such as the size of the swarm relative to the available resources in the surrounding environment and the potential impact on the local ecosystem.

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Answer:

What does it even say? Plus i'm 5th grade sooo, me OUT!

Step-by-step explanation:

The correct models are

7) One sample, Z test of proportion

8) Unequal variance t-test

For the claim that more than 65% of students at De Anza College will transfer, the appropriate model to use is the One sample, Z test of proportion. This model is used when we want to test a claim about a proportion or percentage in a single sample.

For the claim that there is a difference in the standard deviation of hours spent studying per week at De Anza and Foothill College, the appropriate model to use is the Unequal variance t-test. This model is used when comparing the means of two independent samples with unequal variances.

So, the correct models are:

7) One sample, Z test of proportion

8) Unequal variance t-test

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